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Slope Stability Analysis of a Ancient Earthworks

Ashley Evans-Busch1

1 School of Human Evolution and Social Change, Center for Bioarchaeological Research, Arizona State University, Tempe 85281, USA

April 28, 2010

In the Midwest during the Middle Woodland period (250 B.C. to A.D. 50), ancient peoples constructed thousands of earthworks along the tributaries of the Mississippi valley, some of which still stand meters above the surrounding floodplain, but their shape and size have been altered by agricultural processes. Some of the most well preserved and documented sites are found in south-central Ohio, within the Scioto River Valley, and these earthworks have been the focus of archaeological research in exploring the life ways of Middle Woodland peoples. As earthwork construction was import to the Hopewellian peoples, the following article explores the process of earthwork construction drawing from geotechnical engineering design. Like modern engineers, ancient earthwork builders had to weigh the structural advantages of soils with the cost of procuring different soils (i.e. distance to resource, effort of excavation, and ease of transportation). To explore these issues, the following article identifies the physical properties and strength parameters (cohesion and friction angle) of soil found in the vicinity of the Hopewell site embankments. Next, local soil properties were used to determine the slope stability of various potential geometries of the Hopewell embankments. To evaluate the potential slope geometries, each theoretical failure surfaces was compared to an current failure surface identified by geophysical survey. Identifying the original geometry of the embankment walls larger anthropological implications for identifying labor costs, community planning, technological style, and stratigraphies of artifact assemblages.

Keywords: Hopewell earthworks, ancient soils, slope stability

The ancient monumental earthworks found along the Mississippi valley and its tributaries have captivated the imagination of scholars and the public since the early 19th century (Atwater 1820; Squier and Davis 1848). In the Scioto valley of Ohio, Middle Woodland peoples constructed impressive geometric earthen embankments enclosing upwards of 100 acres and embankments standing meters over the valley floor (Figure 1). The sheer size of these remarkable structures suggests large scale planning, designing, and engineering of soil.

Research conducted on ancient structures typically falls into the realm of archaeology, with previous interpretations of earthworks focusing on energetic models (Trigger 1990), power (Nielson 1995; Kolb et al. 2004), world view (Buikstra and Charles 1998), mathematics (Byers 2004), cosmology (Bradley 1998, 2000), and community interaction (Carr and Case 2005, Bernardini 2004) to name just a few. Regardless of the enclosures higher level meaning, the embankment walls were impressive feats of engineering that were built by human hands, by people that had their own knowledge of materials and construction techniques. An aspect of interpretation of the earthworks that should be considered is the process of construction. The field most closely aligned with understanding the processes of construction for earthen structures is geotechnical engineering. Therefore, in the following article, I use an archeo-engineering perspective that utilizes concepts of geotechnical engineering to identify the human ingenuity behind the construction of ancient earthworks.

Fig. 1. Map showing location of earthworks and mounds found in Ohio (red dots), and location of geometric earthworks in the Scioto Valley of Ohio that are mentioned in the article, note the Hopwell earthwork at center.

Case Study

The construction of earthworks in the Eastern Woodlands of North America has a great time depth (~14,000 years) and variety in expression of forms throughout time and geography. The term earthwork, used here, refers to any structure that was created by intentionally depositing layers of soil to modify the natural landscape. The following article focuses on one type of earthwork-- a geometric enclosure. These structures consisted of circular and rectangular designs of earthen embankments that were sinusoidal in cross section and occurred with and without ditches (Figure 1) (Byers 2004). The dimensions and slopes of the existing earthworks are more likely a product of erosion and recent agricultural modification. Interestingly, the Scioto Valley contains the highest number of geometric enclosures in the Eastern Woodlands.

The following analysis considers the Hopewell site earthwork enclosure, which dates to the Middle Woodland period (250 B.C. to A.D. 50). The earthworks site is located on the second terrace of the North Fork of the Paint Creek, at latitude 39.3614 and longitude -83.0897 (Figure 1). As the Hopewell site was considered a type site for the Hopewellian tradition, preservation of the site has left the enclosure largely intact. Although, only sections of the enclosures are visible today, segments of the wall that lie on the forth terrace are well preserved (Figure 2). The site consists of a large square enclosure made of four nearly perpendicular walls that enclose roughly 16 acres; attached to the square enclosure is a rounded enclosure that follows the contours of the third terrace and enclosures roughly 100 acres; enclosed within the rounded enclosure is a semicircular enclosure on a raised platform; and within each enclosure are located numerous burial mounds. The earliest recorded dimensions of the enclosure embankments indicate basal widths of 35 feet and heights of 30 feet, which would have resulted in slopes at a 60 degree angle or greater (Squire and Davis 1848).

Fig. 2. Detail of the Hopewell site showing elevations and locations of the embankments as identified by Squire and Davis (1848), embankment between red arrows and located on the third terrace is well preserved.

Previous Research

Previous excavations at geometric enclosures have been limited to excavation of enclosed mounds, expect for the sites of Hopeton and Newark. Based on excavations at the Hopeton site, earthwork enclosures are assumed to be constructed of multiple soils layers (Lynott 2006). In which, the original topsoil is removed before construction and a thin black organic soil deposited, over which is layered yellow clay loam, red sandy clay, then more yellow clay loam, and a capping layer of brown topsoil. Alternatively, excavations at the Newark site located north-east of the Scioto Valley, revealed a unique construction pattern that entailed first building separate mounds constructed of layers of black, yellow, and brown soil and then filling in the spaces between mounds to create an embankment (Lepper 1998). Regardless of the exact layering of soil, Middle Woodland peoples were obtaining diverse soils from the landscape to create a multi-colored structure.

Drawing on the variation in soil color, Bernardini (2004) identifies the distances between potential sources for the red, yellow, and brown soil compared to each earthwork in the Scioto Valley. The goal of his article was to estimate the size of the labor force needed to construct each earthwork, largely based on resource procurement distance. From an engineering perspective additional factors that may affect labor estimates include soil friability (ease of excavation) and compaction effort (how soil was emplaced). Additionally, the strength properties of a given soil type greatly affect the size and shape of embankment that can be constructed. From a heuristic standpoint, yellow soil is more sand rich, red soil is more clay rich, and brown soil would be more organic rich. Variation in soil color, therefore, implies variation in a given soils chemical, sand, clay, and organic content, all of which affect soil strength.

Alternatively, ONeal et al. (2005) estimates the soil diffusion constant for the embankment walls at the Hopewell site (k=0.0005 m2/yr) as a means to understand site change over time. The soil diffusion constant (k) is a factor that estimates the erosion rate that would result in the current sinusoidal shape of the walls. The calculation of the diffusion constant is based primarily on two geologic factorssediment flux and slope of the soil (Formula 1, Kirby 1971). As calculation of these factors are typically used in geological application the calculations do not account for the initial stability of a given slope from an engineering calculation of strength of the soil (Formula 2, Pierce and Colman 1996):

; ; (1)

where k is the diffusivity constant; q is the sediment flux; dh/dx is the slope gradient; t is time.

(2)

where is the initial scarp slope before erosion; is the soil friction angle; h is the height of scarp; t is time; ERF is the error function.

ONeal et al. (2005) hypothesizes three types of slopes including triangular, trapezoidal, and sinusoidal. However, the hypothesized initial slopes may not have been stable after construction with the assumed clay loam soil used in their analysis. To explore the slope stability, the following analysis considers the shape of the initial slopes in addition to other factors that would have affected the construction of the earthen embankments (Table 1).

Table 1. Factors affecting soil strength

1. initial slopes and height of embankments

2. strength properties of soil used in construction

3. compaction effort imparted on the soil during construction

4. duration of construction

5. stress history of the soil after construction

6. mode of slope failure

7. initial conditions of soil prior to aging over 2000 years

Analysis of Soil Strength

To begin to explore the structural properties of the Hopewell embankment walls, basic soil properties were determined from USDA-NRCS Soil Report and Johnstons (1975) engineering characteristics of Ohio soils. Following the previous studies, soil color was determined from the mussel data provided by the soil survey and mapped in location to the earthwork (Figure 3). Importantly, the variation in soil color corresponds to variation in engineering classification of the soil (Figure 4); in particular the reddish brown soil corresponds with the A-6 classification, while all other brownish soils correspond to A-4 soils.

Evans-BuschSlope Stability Analysis of a 2,000 Year Old Earthwork12

Fig. 3. Map of soil color in proximity of the Hopewell embankments, brown and reddish brown soils make up the majority of soils on the second terrace, whereas yellowish brown and grey soils are found primarily on the third terrace.

Fig. 4. Map of soil properties in proximity of the Hopewell embankments, A-4 (green), A-6 (brown), A-2 (blue), water (white).

The stability of a slope is dependent on the resisting force being greater than the driving force. In the case of the earthwork embankments the frictional and cohesional properties of the soil provided the resistance that withstands the driving forces exerted by weight of the embankment. Frictional properties of the soil are dependent on the grain size distribution, particle shape, and void ratio. Whereas cohesional properties of the soil are dependent on the ionic attraction and chemical cementation between particles. The soils found within seven square miles of the Hopewell site can be generally classified as clayey silt (CL-ML), suggesting that the soil strength is dominated by the cohesive properties of the soil. Importantly, the activity of the soil is low suggesting limited shrink/swell properties of the soil (Figure 5).

Fig. 5 . Volume change tendencies for Hopewell soils, based on Van der Merwe (1964).

Determining the strength properties of soil from soil classification properties produces variable results, but are necessary for initial design considerations. Often general formulas that account for many soils types have large standard deviation ranges (Table 2). Recent research on Ohio soils has produced correlations between soil strength properties and AASHTO classifications (Holko 2008). These correlations were then used to estimate the average shear strength and friction angle for the soils located in the vicinity of the Hopewell earthwork (Table 3, and Appendix).

Table 2. Correlation between soil strength properties and index properties.

Soil Type

Dependent Variable (y)

Independent Variable (x)

Equation

Reference

unknown

Friction angle

Plasticity Index

y = 0.001x2 - 0.276x + 35.89

Terzaghi (1996)

NC soil

Friction angle

Plasticity Index

y = -6.59ln(x) + 50.61

Kenny (1959)

Clay

Undrained Shear Strength

Liquidity Index

y=e^(0.026-1.21x)

Yilmaz (2000)

Unkown

Undrained Shear Strength

California Bearing Ratio

Y=x/0.62

Sukumaran (2000)

NC soil

Undrained Shear Strength

Plasticity Index

y=(0.11+0.003x)*()

Das (1994)

A-4, A6, A-7-6

Effective Friction Angle

Plasticity Index

y = (24.31x + 95.428)/x

Holko (2008)

A-4

Unconfined Comp. Strength

Plasticity Index

y = 6.7863x2 105.25x + 450.32

Holko (2008)

A-6

Unconfined Comp. Strength

% Silt & Dry Unit

Weight

y= -1.7375 (%Silt) + 1.1892

(DUW) 32.4728

Holko (2008)

A-7-6

Unconfined Comp. Strength

% Sand & Plastic Limit

y= 0.8677 (%S) + 9.7743(PL) 154.2631

Holko (2008)

As Holko (2008) correlations were only for unconfined compressive strength, these values were converted to undrained shear strength by use of Das (1999) correlation. Equations based on the California Bearing capacity were not used due to a lack of correlation with the plasticity index, and Yimazs equations were not used due to uncertainties about liquidy index although values were similar to Das calculations. As would be expected values of shear strength and friction angle resulted in results typical of medium to stiff silty-clay (Coduto 2001:89)

Table 3. Soil strength properties calculated from Holko (2008) and averaged by soil color.

Soil Color

Activity (-)

Effective Friction Angle (deg.)

Undrained Shear Strength (kPa)

Yellow

0.2

39.3

62.1

Brown

0.6

32.6

110.5

Grey

0.6

31.6

140.4

Red

0.4

34.9

49.8

Stability of Slopes

There are four possible modes of failure for embankment slopes (Figure 6). As translational (Type 4) failures occur on long slopes; only the toe, base, and slope failure will be considered in the following analysis. Additionally, the initial cross-sectional geometries of the embankments may determine the mode of failure; for example slopes over 53 degrees typically result in toe failure. In the case of the Hopewell embankments, three types of slopes have been hypothesized with geometries corresponding to previous analyses and historic records (Bernardini 2003; ONeal et al. 2005; Squire and Davis 1848) (Figure 7). Unlike previous analyses the following evaluation of slope considers a 6 meter tall embankment. This taller slope height was calculated from a critical height analysis assuming a factor of safety of 2 for the lowest undrained shear strength soil (Berks channery silt loam) (Tersaghi and Peck 1996):

(3)

where Hcritical is the height of the slope; cu is the undrained cohesion; FS is the factor of safety; is the moist unit weight; and m is a factor of slope.

Fig. 6. Types of embankment slope failure including(1) base failure, (2) toe failure, (3) slope failure , and (4) translational movement.

Fig. 7. Hypothesized shape of Hopewell earthworks, showing three hypothesized slope geometries

To evaluate the stability of the hypothesized original slopes of the Hopewell embankments, different geometric configurations, soil properties, and water level conditions were modeled using the UTESASED4 slope stability program. Analysis was conducted on the slope of the embankment and ditch using the simplified bishop method based on undrained shear strength and no friction angle. The underlying soil was assumed to be a Miamian silt loam soil which varies in strength with depth (Figure 7). Additionally, three water level conditions were considered, (1) open ditch with no water, (2) ditch filled with water, (3) no ditch.

Interestingly, all slope conditions modeled were found to be stable with a factor of safety greater than 2. Assuming that these results are based on soil properties that accurately reflect the natural soil conditions that Middle Woodland peoples could have collected, then choice of soils of different colors would not have greatly affected slope stability. The most critical soil color were reddish soils, which had the least variability in strength values and reflects roughly 5% of the soils in the area of the Hopewell site. The use of red soils in Middle Woodland earthworks is assumed to be limited to capping of slopes and lining of ditches (Lynott 2006) and therefore would act to limit erosional forces.

The most stable soil was greyish brown in color, which is interesting due to the potential of higher organic content in these soils. However, these soils are typically found in thin layers (just a few inches thick) at the base of an earthwork and may be evidence of burning prior to construction. Interestingly, layering soils with a capping of red soil, over a layer of yellow, then brown soil, over a thin layer of grey soil, produces a highly stable structure (nearly as stable as using only one soil color).

The most critical water condition occurred when there was no water in the ditch. As the ditches have been dry during recorded history, failure of slopes may have been triggered by fluctuating ground water levels that occurred around the end of the Middle Woodland period as evidenced by a decline in sea water levels

The most critical slope geometry occurred when slopes were the heights (72 degrees) as illustrated by the trapezoidal cross section. The most stable geometry was the triangular geometry, which had the shallowest slopes (50 degrees) and smallest top width. The original shape of the earthworks then is a factor of top width. Leading to questions about the designers intentions and use of the site.

Table 4. Results of slope stability analysis, values indicates factor of safety for a given combination of soil, geometry, and water.

Color

Undrained Shear

Strength

(kPa)

Moist Unit Weight (kN/m3)

Trapezoidal Geometry

(72 deg slope)

Sinusoidal Geometry

(61 deg slope)

Triangular Geometry

(50 deg slope)

Ditch without water

Ditch with water

No Ditch

Ditch without water

Ditch with water

No Ditch

Ditch without water

Ditch with water

No Ditch

Red

49.8

14.7

2.0

2.2

2.8

2.5

2.7

3.2

3.2

3.5

3.7

Yellow

62.1

14.2

2.7

2.5

3.5

2.7

2.9

3.9

3.5

3.7

4.4

Brown

110.5

13.6

3.1

3.8

4.6

3.7

5.4

4.9

4.8

4.8

5.5

Grey

140.4

14.7

3.1

3.8

4.7

4.1

5.2

4.8

4.8

6.4

5.4

Layered

(49.8+16.54(d))

14.2

3.1

3.7

4.6

3.6

3.8

4.9

4.7

4.9

5.5

Consideration of slope failure

As a diversity of slope geometries, soil conditions, and water levels were found to be sable with embankment heights that were historically described (6 meters), the question then turns to what type of slope would produce the current sinusoidal geometry. The above modeled shear surface geometries can then be compared to current conditions of shear failure surfaces to better understand the forces that caused the slope degradation (Figure 8). The condition that most closely matches the current slope failure is a shallow slope (